Queued prompts can start before the active response finishes #28375

Description

When a prompt is submitted while a session is already running, the queued prompt can be picked up by the active loop before the active assistant response has completed.

This breaks the expected turn ordering. The intended behavior is:

1. Active user prompt is sent to the model.
2. Active assistant response completes.
3. Queued user prompt is processed.
4. Queued assistant response completes.

Instead, the queued prompt can be included in the next model input too early, while the first response is still in progress.

Expected behavior

Queued prompts should be persisted and marked as queued, but the queued turn should not be drained into an LLM call until the active prompt loop has finished.

Why this matters

This can cause the model to see future user input before it has finished responding to the current turn, which changes conversation semantics and can produce confusing or out-of-order responses.